Haslegrave, J. and Jordan, J. (2016) Preferential attachment with choice. Random Structures and Algorithms, 48 (4). pp. 751-766. ISSN 1042-9832
Abstract
We consider the degree distributions of preferential attachment random graph models with choice similar to those considered in recent work by Malyshkin and Paquette and Krapivsky and Redner. In these models a new vertex chooses r vertices according to a preferential rule and connects to the vertex in the selection with the sth highest degree. For meek choice, where s > 1, we show that both double exponential decay of the degree distribution and condensation-like behaviour are possible, and provide a criterion to distinguish between them. For greedy choice, where s = 1, we confirm that the degree distribution asymptotically follows a power law with logarithmic correction when r = 2 and shows condensation-like behaviour when r > 2.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2015 Wiley Periodicals, Inc. |
Keywords: | random graphs; preferential attachment; choice |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Science (Sheffield) > School of Mathematics and Statistics (Sheffield) |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 28 Oct 2015 15:04 |
Last Modified: | 22 Feb 2018 15:10 |
Published Version: | https://doi.org/10.1002/rsa.20616 |
Status: | Published |
Publisher: | Wiley |
Refereed: | Yes |
Identification Number: | 10.1002/rsa.20616 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:87911 |